Method and apparatus for image signal processing

ABSTRACT

Image signal processing method and apparatus having a first filter storage portion in which first filters are correlatively stored; a second filter storage portion in which second filters are correlatively stored; a first filter selection portion for selecting a first filter based on the power spectrum of the input image; a second filter selection portion for selecting a second filter based on the SIN (signal-to-noise ratio) of the input image; a third filter creation portion for creating a third filter by summing up the first and second filters; and a convolutional processing portion for convolving the input image using the created third filter.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and apparatus for signalprocessing.

2. Description of Related Art

Techniques for performing image processing such as edge enhancement andblurring using a convolution filter such as a Laplacian filter orGaussian filter are known from the past (see, for example,JP-A-2009-79949).

However, related art techniques do not have any filter that actsprecisely on any arbitrary input image. Consequently, it has beenrequired to use a filter whose parameters have been adjusted by assuminginput images. Furthermore, a wavelet algorithm that expands an inputimage into image elements of plural resolutions is known. The inputimage is expanded into a series of image elements which are half as manyas there are pixels. Therefore, the resolutions differ greatly. Thispresents the problem that it is impossible to finely adjust the imagequality. Another problem with wavelet analysis is that an exorbitantlylong time is required to process a large image because the input imageis expanded.

SUMMARY OF THE INVENTION

In view of the foregoing problems, the present invention has been made.According to some embodiments of the invention, it is possible to offeran image processing method and apparatus capable of acting on andprocessing various input signals in a short time.

(1) A method for signal processing associated with the present inventionstarts with calculating a power spectrum of an input signal. A powerspectrum approximate to the calculated power spectrum is selected from aplurality of power spectra stored in a first filter storage portion. Afirst filter corresponding to the selected power spectrum is selectedfrom a plurality of first filters stored in the first filter storageportion. This processing step may be hereinafter referred to as thefirst filter selection step. Then, the S/N (signal-to-noise ratio) ofthe input signal is calculated. An S/N approximate to the calculated S/Nis selected from a plurality of S/Ns stored in a second filter storageportion. A second filter corresponding to the selected S/N is selectedfrom a plurality of second filters stored in the second filter storageportion. This processing step may be hereinafter referred to as thesecond filter selection step. The selected first and second filters aresummed up to create a third filter. This processing step may behereinafter referred to as the third filter creation step. The inputsignal is convolved using the created third filter. This processing stepmay be hereinafter referred to as the convolution step.

According to the present invention, a first filter selected based on thepower spectrum of an input signal is added to a second filter selectedbased on the S/N of the input signal, thus a third filter is created.The input signal is convolved using the third filter. Consequently, theinput signal can be processed using the filter adapted for the inputsignal in a short time.

(2) In a method for signal processing associated with the presentinvention, the first filters stored in the first filter storage portionhave been created based on sample input signals by a filter creationstep and are correlated with power spectra of the sample input signals.The second filters stored in the second filter storage portion have beencreated by the filter creation step and are correlated with S/Ns of thesample input signals. During the filter creation step, a filter of anarbitrary distribution function G₀ is expanded into a series of n filterelements (where n is an arbitrary number) each of which is thedifference between two distribution functions. The coefficients of thefilter elements are set at will. The filter elements are multiplied bytheir respective coefficients and summed up. Thus, the first filter thatis a function of the number of the filter elements n and of thecoefficients of the filter elements is created. The distributionfunction G_(n) of the nth order is obtained when the filter is expandedinto the arbitrary number n of filter elements. The distributionfunction G_(n) and the distribution function G₀ are combined witharbitrary weight coefficients to create second filters. The value of thenumber n, the coefficients of the filter elements, and the weightcoefficients may be set based on the sample input signals.

According to the present invention, the first filter adapted for thesample input signal can be created by setting the value of the number nand the coefficients of the filter elements based on the sample inputsignal. Furthermore, the second filter adapted for the sample inputsignal can be created by setting the value of the number n and theweight coefficient based on the sample input signal. Plural firstfilters and plural second filters are created based on sample inputsignals. A first filter selected from the created first filters based ona power spectrum of an input signal and a second filter selected fromthe created second filters based on the S/N of the input signal aresummed up to create a third filter. The input signal is convolved usingthe third filter. Consequently, signal processing can be performed in ashort time using the filter adapted for the input signal.

(3) In the signal processing method associated with the presentinvention, during the filter creation step, the value of the number n,the coefficients of the filter elements, and the weight coefficients maybe set to maximize the S/Ns of the signals obtained by convolving thesample input signals using the created first and second filters.

According to the present invention, the first and second filters adaptedfor the sample input signal can be created.

(4) In the method of signal processing associated with the presentinvention, each of the distribution functions may be a Gaussianfunction.

Furthermore, the distribution function G_(n) of the nth order may be aGaussian function. The distribution function G₀ may be a functionapproximate to a delta function.

(5) An apparatus for signal processing associated with the presentinvention has: a first filter storage portion in which first filterscreated based on sample input signals and power spectra of the sampleinput signals are correlatively stored; a second filter storage portionin which second filters created based on sample input signals and S/Nsof the sample input signals are correlatively stored; a first filterselection portion for calculating a power spectrum of an input signal,selecting a power spectrum approximate to the calculated power spectrumfrom the power spectra stored in the first filter storage portion, andselecting a first filter corresponding to the selected power spectrumfrom the first filters stored in the first filter storage portion; asecond filter selection portion for calculating an S/N of the inputsignal, selecting an S/N approximate to the calculated S/N from the S/Nsstored in the second filter storage portion, and selecting a secondfilter corresponding to the selected S/N from the second filters storedin the second filter storage portion; a third filter creation portionfor creating a third filter by summing up the selected first and secondfilters; and a convolutional processing portion for convolving the inputsignal using created third filter.

According to the present invention, a first filter selected based on thepower spectrum of the input signal and a second filter selected based onthe S/N of the input signal are summed up to create a third filter. Theinput signal is convolved using the third filter. Consequently, signalprocessing can be performed in a short time using a filter adapted forthe input signal.

(6) The apparatus for signal processing associated with the presentinvention may further include a filter creation portion for creating thefirst and second filters based on the sample input signals andcalculating power spectra and S/Ns of the sample input signals. Thefilter creation portion may expand a filter of an arbitrary distributionfunction G₀ into a series of n filter elements (where n is an arbitrarynumber) each of which is the difference between two distributionfunctions, set coefficients of the filter elements at will, multiply thefilter elements by the coefficients, respectively, sum up the multipliedfilter elements to create a first filter that is a function of thenumber of the filter elements n and of the coefficients of the filterelements, obtain a distribution function G_(n) of the nth order when thefilter is expanded into the n filter elements, combine together thedistribution function G_(n) and the distribution function G₀ with anarbitrary weight coefficient to obtain a second filter, and set thevalue of the number n, the coefficients of the filter elements, and theweight coefficients based on the sample input signals.

According to the present invention, first filters adapted for sampleinput signals can be created by setting the value of the number n andthe coefficients of the filter elements based on the sample inputsignals. Second filters adapted for sample input signals can be createdby setting the value of the number n and the weight coefficient based onthe sample input signals. A first filter is selected according to apower spectrum of an input signal from the first filters created basedon the sample input signals. A second filter is selected according to anS/N of the input signal from the second filters created on the basis ofthe sample input signals. The selected first and second filters aresummed up to create a third filter. The input signal is convolved usingthe third filter. Consequently, signal processing can be performed in ashort time using the filter adapted for the input signal.

(7) In the apparatus for signal processing associated with the presentinvention, the filter creation portion may set the value of the numbern, the coefficients of the filter elements, and the weight coefficientsto maximize the S/Ns of the signals obtained by convolving the sampleinput signals using the created first and second filters.

According to the present invention, the first and second filters adaptedfor sample input signals can be created.

(8) In the apparatus for signal processing associated with the presentinvention, each of the distribution functions may be a Gaussianfunction.

Furthermore, the distribution function G_(n) of the nth order may be aGaussian function. The distribution function G₀ may be a functionapproximate to a delta function.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of an image processing apparatus(one example of signal processing apparatus) associated with oneembodiment of the present invention.

FIG. 2 is a detailed functional block diagram of the filter creationportion of the apparatus shown in FIG. 1.

FIG. 3 shows examples of filter element obtained by expansion.

FIG. 4 is a graph illustrating the coefficients of the filter elements.

FIG. 5 shows one example of second filter.

FIG. 6 shows one example of intermediate filter.

FIG. 7 is a flowchart illustrating one example of a sequence ofoperations performed by one embodiment of the invention.

FIG. 8 is a flowchart illustrating one example of a sequence ofoperations performed by one embodiment of the invention.

FIGS. 9A and 9B are images illustrating one example of image processingmethod according to the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The preferred embodiments of the present invention are hereinafterdescribed in detail with reference to the drawings. It is to beunderstood that embodiments described below do not unduly restrict thecontents of the invention delineated by the appended claims and that allthe configurations described below are not always essential constituentcomponents of the present invention.

1. Configuration

FIG. 1 is a functional block diagram of an image processing apparatusassociated with one embodiment of the present invention, the imageprocessing apparatus being one example of signal processing apparatus.Note that some of the constituent elements of the image processingapparatus of the present embodiment shown in FIG. 1 may be omitted.

The image processing apparatus, generally indicated by reference numeral1, of the present embodiment is an apparatus for performing imageprocessing to vary the image quality (resolution) of an input SEM imagethat is represented by an input signal and taken by a scanning electronmicroscope (SEM). The apparatus is configured including a filtercreation portion 10, a first filter storage portion 20, a second filterstorage portion 22, a first filter selection portion 30, a second filterselection portion 32, and a third filter creation portion 50, and aconvolutional processing portion 40. The functions of the filtercreation portion 10, the first filter selection portion 30, the secondfilter selection portion 32, the third filter creation portion 50, andthe convolutional processing portion 40 can be accomplished by variousprocessors (such as CPU and DSP) or computer programs. The functions ofthe first filter storage portion 20 and the second filter storageportion 22 can be realized by a RAM, a hard disk, or the like.

The filter creation portion 10 creates first and second filters based ona sample image represented by a sample input signal, calculates a powerspectrum and the signal-to-noise ratio (S/N) of the sample image,outputs the created first filter and the calculated power spectrum tothe first filter storage portion 20, and outputs the created secondfilter and the calculated S/N to the second filter storage portion 22.

The filter creation portion 10 expands a filter that is an arbitrarydistribution function G₀ (e.g., a function approximate to a deltafunction) into a series of n filter elements (where n is an arbitrarynumber) each of which is the difference between two distributionfunctions (e.g., two-dimensional Gaussian functions), sets thecoefficients of the filter elements at will, multiplies the filterelements by the coefficients, adds up the multiplied filter elements tocreate a first filter that is a function of the number of the filterelements n and the coefficients of the filter elements, and sets thenumber of the filter elements n and the coefficients of the filterelements based on a sample image. The filter creation portion 10combines the distribution function G_(n) of the nth order obtained whenthe filter is expanded into the n filter elements and the distributionfunction G₀ with an arbitrary weight coefficient to create a secondfilter. The filter creation portion sets the value of the number n andthe weight coefficient based on the sample input signal.

The filter creation portion 10 sets the value of the number n, thecoefficients of the filter elements, and the weight coefficient tomaximize the S/N of the signal obtained by convolving the sample imageusing the created first and second filters.

First filters created based on sample images by the filter creationportion 10 and power spectra of the sample images are correlativelystored in the first filter storage portion 20. Second filters createdbased on the sample images by the filter creation portion 10 and S/Ns ofthe sample images are correlatively stored in the second filter storageportion 22. Preferably, a number of (e.g., about 100) sets of firstfilters created from sample images and respective power spectra of thesample images are stored in the first filter storage portion 20.Preferably, a number of (e.g., about 100) sets of second filters createdfrom sample images and respective S/Ns of the sample images are storedin the second filter storage portion 22. The sample images can be SEMimages taken from various samples and images of natural objects andartificial objects taken by a digital camera. In the present invention,multiple sets of such first filters and power spectra are previouslystored in the first filter storage portion 20. Multiple sets of suchsecond filters and S/Ns are previously stored in the second filterstorage portion 22.

The first filter selection portion 30 calculates a power spectrum of aninput image (represented by input signals) to be processed, selects apower spectrum approximate to the calculated power spectrum from powerspectra stored in the first filter storage portion 20, selects a firstfilter corresponding to the selected power spectrum from the firstfilters stored in the first filter storage portion 20, and outputs theselected first filter to the third filter creation portion 50.

The second filter selection portion 32 calculates the S/N of the inputimage represented by the input signal, selects an S/N approximate to thecalculated S/N from the S/Ns stored in the second filter storage portion22, selects a second filter corresponding to the selected S/N from thesecond filters stored in the second filter storage portion 22, andoutputs the selected second filter to the third filter creation portion50.

The third filter creation portion 50 adds up the first and secondfilters selected in this way to create a third filter and outputs thecreated third filter to the convolutional processing portion 40.

The convolutional processing portion 40 convolves the input image usingthe third filter generated by the third filter creation portion 50.Furthermore, the convolutional processing portion 40 may convolve aninput image, whose image size (spatial size) has been expanded by animage size expansion portion (not shown), using a selected filter. Aspatial size restoration portion (not shown) may restore the spatialsize of the output image convolved by the convolutional processingportion 40 to the spatial size of the input image.

2. Technique of Present Embodiment

The technique of the present embodiment is next described by referringto drawings.

2-1. Selection of First and Second Filters and Convolution

The image quality of an input image to be processed can be varied byconvolving the input image using a filter of a distribution function.The convolutional processing portion 40 of the present embodimentperforms convolutional processing as given by:I_(out)=F₀

I_(in)  (1)where I_(in) indicates an input image, I_(out) indicates an outputimage, and F₀ indicates a third filter generated by the third filtercreation portion 50. Eq. (1) can be rewritten as follows:

$\begin{matrix}{{I_{out}\left( {x,y} \right)} = {\underset{X,{Y \in R}}{\int\int}{I_{i\; n}\left( {{x - X},{y - Y}} \right)} \times {F_{0}\left( {X,Y} \right)}{\mathbb{d}X}{\mathbb{d}Y}}} & (2)\end{matrix}$where x and y indicate the X- and Y-coordinates, respectively, of theinput image, and X and Y indicate the X- and Y-coordinates,respectively, of the third filter. Usually, the input image isrepresented by discrete values and so Eq. (2) can be rewritten asfollows:

$\begin{matrix}{{I_{out}\left( {{nx},{ny}} \right)} = {\sum\limits_{NX}\;{\sum\limits_{NY}\;{{I_{i\; n}\left( {{{nx} - {NX}},{{ny} - {NY}}} \right)} \times {F_{0}\left( {{NX},{NY}} \right)}}}}} & (3)\end{matrix}$where nx and ny indicate the numbers of pixels of the input image in theX- and Y-directions, respectively, and NX and NY indicate the numbers ofpixels of the third filter in the X- and Y-directions, respectively.

The first filter selection portion 30 of the present embodiment operatesto perform a discrete Fourier transform of the discrete input imageI_(in) {ij} using:

$\begin{matrix}{F_{pq} = {\sum\limits_{j = 1}^{ny}\;{\sum\limits_{i = 1}^{nx}\;{I_{i\; n}\left\{ {ij} \right\}\exp\left\{ {{- J}\; 2\;{\pi\left( {\frac{p \times \left( {{\mathbb{i}} + 1} \right)}{n\; x} + \frac{q \times \left( {j - 1} \right)}{ny}} \right)}} \right\}}}}} & (4)\end{matrix}$where J=√{square root over (−1)}.

Then, the first filter selection portion 30 calculates the powerspectrum PS_(in)(p,q) of the input image using:PS _(in)(p,q)=√{square root over (Re(F _(pq))² +Im(F _(pq))²)}{squareroot over (Re(F _(pq))² +Im(F _(pq))²)}  (5)

The first filter selection portion 30 computes the error, err, betweenthe power spectrum PS_(in)(p,q) of the input image and each powerspectrum PS(p,q) stored in the first filter storage portion 20 using theequation:

$\begin{matrix}{{err} = \sqrt{\sum\limits_{q = 1}^{ny}\;{\sum\limits_{p = 1}^{nx}\;\left( {{{PS}_{i\; n}\left\{ {p,q} \right\}} - {{PS}\left\{ {p,q} \right\}}} \right)^{2}}}} & (6)\end{matrix}$

The first filter selection portion 30 then selects one of the powerspectra stored in the first filter storage portion 20 which minimizesthe error, err, with the power spectrum of the input image, selects oneof the first filters F_(ex) stored in the first filter storage portion20 which corresponds to the selected power spectrum, and outputs theselected spectrum and first filter to the third filter creation portion50.

The second filter selection portion 32 of the present embodimentcalculates the signal-to-noise ratio, SN_(in), of the input image I_(in)using the formula:

$\begin{matrix}{{SN}_{i\; n} = \frac{\mu_{signal}}{\sigma_{noise}}} & (7)\end{matrix}$where μ_(signal) is the average of the input signal I_(in) and σ_(noise)is the standard deviation of the input signal I_(in) as given by:

$\begin{matrix}{\mu_{signal} = \frac{\sum\limits_{q = 1}^{ny}\;{\sum\limits_{p = 1}^{nx}\;{I_{i\; n}\left( {p,q} \right)}}}{{nx} \times {ny}}} & (8) \\{\sigma_{noise}^{2} = {\frac{1}{{nx} \times {ny}}{\sum\limits_{q = 1}^{ny}\;{\sum\limits_{p = 1}^{nx}\;\left( {{I_{i\; n}\left( {p,q} \right)} - \mu_{signal}} \right)^{2}}}}} & (9)\end{matrix}$

The second filter selection portion 32 then calculates the error, err,between the signal-to-noise ratio, SN_(in), of the input image and eachsignal-to-noise, SN, stored in the second filter storage portion 22using:err=(SN _(in) −SN)²  (10)

The second filter selection portion 32 selects the S/N which minimizesthe error, err, with the S/N of the input image from S/Ns stored in thesecond filter storage portion 22, selects the second filter F_(ex) whichcorresponds to the selected S/N from the second filters stored in thesecond filter storage portion 22, and outputs the selected S/N andsecond filter F_(ex) to the third filter creation portion 50.

The third filter creation portion 50 adds up the selected first filterF_(ex) and second filter F_(ex) to generate a third filter F₀, andoutputs the generated third filter F₀ to the convolutional processingportion 40.

According to the present embodiment, a filter optimal for an input imagecan be obtained in a short processing time without repeating aprocessing operation for generating a filter adapted for the input imageby selecting a first filter corresponding to a power spectrum mostapproximate to the power spectrum of the input image to be processed andselecting a second filter corresponding to an S/N most approximate tothe S/N of the input image.

2-2. Creation of First and Second Filters

FIG. 2 is a detailed functional block diagram of the filter creationportion 10 of the present embodiment.

The filter creation portion 10 includes a filter expansion portion 11, afilter element storage portion 13, a coefficient creation portion 14, afilter reconfiguration portion 15, a convolution portion 16, an imagequality evaluation portion 17, a power spectrum calculating portion 18,and an S/N calculating portion 19.

The filter expansion portion 11 expands a filter of an arbitrarydistribution function G₀ into a series of n filter elements (where n isan arbitrary number) each of which is the difference between twodistribution functions.

Let G_(k) be a two-dimensional distribution function (where k=0, 1, 2, .. . , n (integer)). It is assumed that as the integer k increases, thestandard deviation σ_(k) of the distribution function G_(k) increases.It is here assumed that the distribution function G_(k) is adistribution function of the kth order. For example, if the distributionfunction G_(k) is a two-dimensional Gaussian function, the distributionfunction G_(k) and its standard deviation σ_(k) are given by:

$\begin{matrix}{{G_{k}\left( {x,y} \right)} = {\frac{1}{2{\pi\sigma}_{k}}{\exp\left( {- \frac{x^{2} + y^{2}}{2\sigma_{k}}} \right)}}} & (11) \\{{\sigma_{k} = {{\left( {k - 1} \right)\Delta\;\sigma} + {\sigma_{k}\mspace{31mu}\left( {k \geq 1} \right)}}}{\sigma_{k} = {\sigma_{0} \cong {0\mspace{31mu}\left( {k = 0} \right)}}}} & (12)\end{matrix}$

If k=0 as given by Eq. (12), G₀ is approximate to a delta function(i.e., the dispersion σ₀ of G₀ is approximate to 0).

In the present embodiment, the distribution function G₀ approximate tothe delta function is expanded into the sum of the distribution functionG_(n) of the nth order and a series of n filter elements each of whichis a distribution function being the difference between two distributionfunctions. In this example, the distribution function G₀ is expanded asfollows:G ₀ =G _(n)+(G ₀ −G _(n))  (13)

Expanding the second term of the right side of Eq. (13) similarly into nterms gives rise to:

$\begin{matrix}\begin{matrix}{G_{0} = {G_{n} + \left( {G_{0} - G_{n}} \right)}} \\{= {G_{n} + \left( {G_{0} - G_{1}} \right) +}} \\{\left( {G_{1} - G_{2}} \right) + {\left( {G_{2} - G_{3}} \right)\mspace{11mu}\ldots} +} \\{\left( {G_{n - 1} - G_{n}} \right)}\end{matrix} & (14)\end{matrix}$

Assuming that the kth expansion term is a filter element M_(k) of thekth order and that the equation M_(k)=G_(k-1)−G_(k) holds, Eq. (14) canbe rewritten as:

$\begin{matrix}{G_{0} = {G_{n} + {\sum\limits_{k = 1}^{n}\; M_{k}}}} & (15)\end{matrix}$

As can be seen from Eq. (15), the distribution function G₀ has beenexpanded into the distribution function G_(n) of the nth order and nfilter elements M_(k) (k=1 to n) each of which is the difference betweenthe distribution function G_(k-1) of the (k−1)th order and thedistribution function G_(k) of the kth order. As described later, thedistribution function G_(n) of the nth order is used when the secondfilter that is a noise filter is created. The n filter elements M_(k)are used when the first filter being an edge enhancement filter iscreated.

Examples of the filter elements M_(k) are shown in FIG. 3, where Δσ=0.5,σ₁=1.5, and k=1, 3, and 5 in Eq. (12).

As shown in FIG. 3, each filter element M_(k) is a differential filterthat emphasizes the edges of the input image in the kth order. As thevalue of k of each filter element M_(k) is increased, its dispersionincreases. Therefore, a filter element M_(k) having a small value of kacts as an edge enhancement filter acting on higher-frequency componentsof the input image. On the other hand, a filter element M_(k) having agreater value of k acts as an edge enhancement filter acting onlower-frequency components of the input image.

The filter element storage portion 13 shown in FIG. 2 stores thedistribution function G₀, the nth-order distribution function G_(n)generated by the filter expansion portion 11, and the n filter elementsM_(k).

The coefficient creation portion 14 creates coefficients ω_(k) by whichthe n filter elements M_(k) stored in the filter element storage portion13 are respectively multiplied, for example, using the followingformula:ω _(k)=λ^(n-k)  (16)where λ is an arbitrary real number and preferably assumes a positivevalue from approximately 0.5 to 0.9. In the present embodiment, λ is areal number less than unity. Therefore, a filter element M_(k) (a filterelement acting on low-frequency components of the image) having a largevalue of k has a large value of coefficient ω_(k) as shown in FIG. 4. Onthe other hand, a filter element M_(k) (a filter element acting onhigh-frequency components of the image) having a small value of k has asmall value of coefficient ω_(k). That is, a filter element M_(k) actingon higher-frequency components has the coefficient ω_(k) whose value isattenuated to a greater extent, because power spectra of input imagesgenerally have large amounts of low frequency components. This canimprove the resolution of the image while maintaining the apparentnaturalness.

As shown in FIG. 4, when the value of λ is varied, the coefficient ω_(k)is attenuated to a different degree. For example, as the value of λ isincreased, the coefficient ω_(k) is less attenuated, and the coefficientω_(k) of the filter element M_(k) acting on higher-frequency componentsof the image can be increased. Conversely, as the value of λ is reduced,the coefficient ω_(k) is more attenuated, and the coefficient ω_(k) ofthe filter element M_(k) acting on higher-frequency components of theimage can be reduced. That is, by varying the value of λ, the weight ofeach filter element M_(k) acting on each frequency component of theimage can be varied. FIG. 4 shows an example in which n=10.

Where one wants to perform image processing such as edge enhancement oncertain frequency components of an input image, the coefficients ω_(k)of filter elements M_(k) acting on these frequency components are set tononzero real numbers, and the coefficients ω_(k) of the other filterelements M_(k) are set to 0.

The filter reconfiguration portion 15 shown in FIG. 2 reconfigures afirst filter F_(e)(n,λ) that is a function of the number of filterelements n and of λ featuring the coefficients ω_(k), based on the nfilter elements M_(k) (k=1 to n) stored in the filter element storageportion 13 and on the coefficients ω_(k) (k=1 to n) generated by thecoefficient creation portion 14, using the following equation:

$\begin{matrix}{{F_{e}\left( {n,\lambda} \right)} = {\sum\limits_{k = 1}^{n}\;{\varpi_{k} \times {{Norm}\left( M_{k} \right)}}}} & (17)\end{matrix}$where Norm ( ) indicates normalization.

The first filter F_(e)(n,λ) having various characteristics depending onthe values of λ and n can be created by adding up n filter elementsM_(k) (k=1 to n) multiplied by the coefficients ω_(k) based on λ so asto reconfigure a first filter that is an edge enhancement filter in thisway. For example, as shown in FIG. 4, it is possible to create the firstfilter F_(e)(n,λ) having filter elements M_(k) which act onhigher-frequency components and on which greater weights are attached byincreasing the value of λ. Furthermore, the first filter F_(e)(n,λ)acting on lower-frequency components can be created by increasing thevalue of the number n.

The filter reconfiguration portion 15 reconfigures a second filterF_(c)(n,α), based on the distribution function G₀ approximate to a deltafunction and on the distribution function G_(n) of the nth order, thefunctions being stored in the filter element storage portion 13, by theuse of the following equation:F _(c)(n,α)=(1−α)×Norm(G ₀)+Norm(G _(n))  (18)where α is a weight coefficient having a value from 0 to 1. The secondfilter F_(c)(n,α) having different characteristics according to thevalues of n and a can be created by combining together the distributionfunction G₀ and the nth-order distribution function G_(n) using thearbitrary weight coefficient α so as to reconfigure the second filterbeing a noise filter in this way.

An example of the second filter F_(c)(n,α) is shown in FIG. 5. As shownin FIG. 5, in this second filter F_(c)(n,α), high intensity portions aredistributed around the center. Low intensity portions are distributed inlong tail portions. This filter acts as a noise filter (blur filter) forremoving noise from the input image.

As shown in FIG. 5, the level of filtering of the second filterF_(c)(n,α) shows a distribution function G₀ that approximates a deltafunction more closely as the value of the weight coefficient α isreduced. The distribution more closely approaches the nth-orderdistribution function G_(n) that is a Gaussian function as the value ofthe weight coefficient α is increased. That is, the noise filteringaction of the second filter F_(c)(n,α) can be weakened by reducing thevalue of the weight coefficient α, and vice versa. Furthermore, sincethe dispersion of the distribution function G_(n) increases withincreasing the value of n, the second filter F_(c)(n,α) can be sodesigned as to act on higher-frequency components of the input image byreducing the value of n. The second filter F_(c)(n,α) can be designedsuch that it acts on the low-frequency components of the input image byincreasing the value of n.

In the technique of the present embodiment, filter elements having asmall size compared with the input image (e.g., 9×9 filter elements) arearranged and expanded to reconfigure each of the first and secondfilters. Therefore, the processing time can be much shortened comparedwith a wavelet technique in which the input image itself is expanded.

The filter reconfiguration portion 15 adds up the first filterF_(e)(n,λ) and second filter F_(c)(n,α) to create an intermediate filter{tilde over (M)}(n,λ,α) for evaluation, using the following equation:{tilde over (M)}(n,λ,α)=F _(e)(n,λ)+F _(c)(n,α)  (19)

An example of the intermediate filter {tilde over (M)}(n,λ,α) is shownin FIG. 6. The third filter F₀ created by the third filter creationportion 50 is similar to the intermediate filter {tilde over(M)}(n,λ,α). As shown in FIG. 6, the intermediate filter {tilde over(M)}(n,λ,α) acts as an edge enhancement filter for emphasizing the edgesof the input image and also as a noise filter for removing noise fromthe input image. Furthermore, as shown in FIG. 6, the intermediatefilter {tilde over (M)}(n,λ,α) acts more as an edge enhancement filterwith reducing the value of the weight coefficient α. The intermediatefilter acts more as a noise filter with increasing the value of theweight coefficient α.

The convolution portion 16 shown in FIG. 2 creates an image I_(C) byconvolving the sample image I_(in) using the intermediate filter {tildeover (M)}(n,λ,α) as given by the following formula, the intermediatefilter {tilde over (M)}(n,λ,α) being created by the filterreconfiguration portion 15.I _(c) ={tilde over (M)}(n,λ,α)

I _(in)  (20)

The image quality evaluation portion 17 similarly calculates the S/N ofthe image I_(c) created by the convolution portion 16 using Eq. (7).

The convolution portion 16 creates the images by convolving a sampleimage using the intermediate filter {tilde over (M)}(n,λ,α) about allthe combinations of n, λ, and α of the intermediate filter {tilde over(M)}(n,λ,α). The image quality evaluation portion 17 calculates the S/Nsof the created images I_(c) and finds a combination of n, λ, and a thatgives a maximum value of S/N using the following equation. The firstfilter F_(e)(n,λ) having a combination of n and λ that gives a maximumS/N is output as the first filter F_(c) optimal for the sample image tothe first filter storage portion 20 (see FIG. 1). The second filterF_(c)(n,α) having a combination of n and α that gives a maximum S/N isoutput as the second filter F_(c) optimal for the sample image to thesecond filter storage portion 22 (see FIG. 1).SN→arg·max{SN|∀n,∀λ,∀α}  (21)

The power spectrum calculating portion 18 calculates a power spectrum,PS, of a sample spectrum similarly to the case using Eq. (5) and outputsthe calculated spectrum to the first filter storage portion 20. Theoptimum first filter F_(e) created based on the sample image and thepower spectrum PS of the sample image are correlatively stored in thefirst filter storage portion 20.

The S/N calculating portion 19 calculates the S/N, SN, of a sample imagesimilarly to the case where Eq. (7) is used and outputs the result tothe second filter storage portion 22. An optimum second filter F_(c)created based on the sample image and S/N, SN, of the sample image arecorrelatively stored in the second filter storage portion 22.

The processing consisting of creating the first filter F_(e) and secondfilter F_(c) from the sample image and calculating the power spectrum PSand S/N of the sample image in this way is carried out for pluraldifferent sample images.

According to the present embodiment, it is possible to create the firstfilters F_(e) and second filters F_(c) which are optimal for the sampleimages among the first filters F_(c)(n,λ) and second filters F_(c)(n,α)having various characteristics according to the values of n, λ, and α.

First filters (edge enhancement filters) adapted for input images havingpower spectra approximate to power spectra of sample images can beeasily selected by storing first filters F_(e) optimal for the sampleimages correlatively with the power spectra of the sample images.Furthermore, second filters (noise filters) adapted for input imageshaving S/Ns approximate to S/Ns of sample images can be easily selectedby storing second filters F_(c) optimal for the sample imagescorrelatively with the S/Ns of the sample images. In addition, imageprocessing can be performed by the use of a filter which is optimal foran input image and which acts as an edge enhancement filter and as anoise filter by convolving the input image using a third filter createdby summing up the selected first and second filters.

For example, in response to an input image having a large amount ofhigh-frequency components, a first filter having a large value of λ anda small value of n is selected as an optimum first filter. As a result,a third filter more effectively acting on high-frequency components iscreated as a filter optimal for the input image. On the other hand, inresponse to an input image having a large amount of low-frequencycomponents, a first filter having a small value of λ and a large valueof n is selected as an optimum first filter. As a result, a third filtermore effectively acting on low-frequency components is created as afilter optimal for the input image.

In response to an input image having a high S/N, a second filter havinga small value of α is selected as an optimum second filter.Consequently, a third filter (see FIG. 6) acting mainly as an edgeenhancement filter is created as a filter optimal for the input image.On the other hand, in response to an input image having a low S/N, asecond filter having a large value of α is selected as an optimum secondfilter. As a result, a third filter (see FIG. 6) acting mostly as anoise filter is created as a filter optimal for the input image.

3. Processing

One example of the processing performed in the present embodiment isnext described by referring to the flowcharts of FIGS. 7 and 8. FIG. 7is a flowchart illustrating examples of a filter selection process andconvolutional processing.

First, the first filter selection portion 30 calculates a power spectrumof an input image I_(in) using Eq. (5) (step S10). Then, the selectionportion 30 calculates the error, err, between the power spectrum of theinput image I_(in) and each power spectrum stored in the first filterstorage portion 20 using Eq. (6) (step S12). The selection portionselects the first filter F_(ex) corresponding to the power spectrum thatminimizes the error, err, with the power spectrum of the input imageI_(in) from the power spectra stored in the first filter storage portion20 and reads the selected filter from the storage portion 20 (step S14).

Then, the second filter selection portion 32 calculates the S/N of theinput image I_(in) using Eq. (7) (step S16). The selection portion 32then computes the error, err, between the S/N of the input image I_(in)and each S/N stored in the second filter storage portion 22 using Eq.(10) (step S18). The selection portion selects a second filter F_(ex)corresponding to the S/N that minimizes the error, err, with the S/N ofthe input image I_(in) from S/Ns stored in the second filter storageportion 22, and reads the selected filter from the second filter storageportion 22 (step S20).

The third filter creation portion 50 then adds up the first filterF_(ex) selected in step S14 and the second filter F_(ex) selected instep S20 to create a third filter F_(o) (step S22).

The convolutional processing portion 40 convolves the input image I_(in)using the third filter F_(o) created in step S22 to generate an outputimage I_(out) (step S24).

FIG. 8 is a flowchart illustrating one example of processing performedby the filter creation portion 10.

First, the filter creation portion 10 expands a filter G₀ that is adistribution function approximate to a delta function into adistribution function G_(n) of the nth order and n filter elements M_(k)each of which is the difference between a distribution function G_(k-1)of the (k−1)th order and a distribution function G_(k) of the kth orderusing Eq. (15) (step S30).

Then, n and λ are set to 1 and 0.5, respectively. α is set to Δα(0<Δα<1; for example, Δα=1) (step S32). The coefficients ω_(k) of thefilter elements M_(k) (k=1 to n) are computed using Eq. (16) (step S34).

Then, the first filter F_(e)(n,λ) is reconfigured by adding up togetherthe n filter elements M_(k) multiplied by the coefficients ω_(k) usingEq. (17) (step S36). Then, the second filter F_(c)(n,α) is reconfiguredby combining together the nth-order distribution function G_(n) and thedistribution function G₀ with the weight coefficient α using Eq. (18)(step S38).

Then, the first filter F_(e)(n,λ) and the second filter F_(c)(n,α) areadded up to create the intermediate filter {tilde over (M)}(n,λ,α) usingEq. (19) (step S40).

Then, the sample image is convolved using the intermediate filter {tildeover (M)}(n,λ,α) through Eq. (20) to generate the image I_(C) (stepS42). The S/N of the generated image I_(c) is calculated using Eq. (7)(step S44).

Then, a decision is made as to whether the value of n has reached agiven maximum value, nmax (step S46). If not so, the value of n isincremented by 1 (step S48) and then control proceeds to step S34. Theprocessing subroutine starting with step S34 is repeatedly carried outuntil the value of n reaches the maximum value, nmax.

If the decision at step S46 is that the value of n has reached themaximum value, nmax, a decision is made as to whether the value of λ hasreached 0.9 (step S50). If the decision is NO, the value of λ isincremented by Δλ (step S52) and control goes to step S34. Theprocessing subroutine starting with step S34 is repeatedly performeduntil the value of λ reaches 0.9.

If the decision at step S50 is YES (i.e., the value of λ has reached0.9), a decision is made as to whether the value of α has reached agiven maximum value, αmax (e.g., αmax=1) (step S54). If the decision atstep S54 is NO, the value of α is incremented by Δα (step S56) andcontrol proceeds to step S34. Then, the processing subroutine startingwith step S34 is repeatedly performed until the value of αreaches αmax.

If the decision at step S54 is YES (i.e., the value of α has reachedαmax (that is, the S/N of the image I_(c) has been calculated for allthe combinations of n, λ, and α)), the first filter F_(e)(n,λ) having acombination of n and λ, giving a maximum S/N is taken as an optimumfirst filter F_(e) and output to the first filter storage portion 20. Asecond filter F_(c)(n,α) having a combination of n and α that gives amaximum S/N is taken as an optimum second filter F_(c) and output to thesecond filter storage portion 22 (step S58).

Power spectra of sample images are then calculated using Eq. (5) andoutput to the first filter storage portion 20. The S/Ns of the sampleimages are calculated using Eq. (7) and output to the second filterstorage portion 22 (step S60).

4. Example of Image Processing

FIG. 9A shows one example of SEM image. FIG. 9B shows an output imageobtained as a result of image processing of the input image that is theSEM image shown in FIG. 9A by the technique of the present embodiment.As shown in FIG. 9B, the technique of the present embodiment permitsappropriate edge enhancement and noise removal of the input image.Consequently, the image quality (resolution) of the input image can beimproved.

It is to be understood that the present invention is not restricted tothe above embodiment but rather various changes and modifications may bemade. The present invention embraces configurations substantiallyidentical (e.g., in function, method, and results or in purpose andadvantageous effects) with the configurations described in the preferredembodiment of the invention. Furthermore, the invention embracesconfigurations described in the embodiment and including portions whichhave non-essential portions replaced. In addition, the inventionembraces configurations which produce the same advantageous effects asthose produced by the configurations described in the preferredembodiment or which can achieve the same objects as the configurationsdescribed in the preferred embodiment. Further, the invention embracesconfigurations which are similar to the configurations described in thepreferred embodiment except that well-known techniques have been added.

For instance, in the above embodiment, the present invention is appliedto a case where image processing is applied to two-dimensional images.The invention can also be applied to signal processing ofone-dimensional signal (such as audio signal).

Having thus described my invention with the detail and particularityrequired by the Patent Laws, what is desired protected by Letters Patentis set forth in the following claims.

The invention claimed is:
 1. A method for signal processing, comprisingthe steps of: calculating a power spectrum of an input image signal;selecting a power spectrum approximate to the calculated power spectrumfrom a plurality of power spectra stored in a first filter storageportion; selecting a first filter corresponding to the selected powerspectrum from a plurality of first filters stored in the first filterstorage portion; calculating a S/N (signal-to-noise ratio) of the inputsignal; selecting a S/N approximate to the calculated S/N from aplurality of S/Ns stored in a second filter storage portion; selecting asecond filter corresponding to the selected S/N from a plurality ofsecond filters stored in the second filter storage portion; creating athird filter by adding up the selected first and second filters; andconvolving the input signal using the created third filter.
 2. A methodfor signal processing as set forth in claim 1, wherein the first filtersstored in said first filter storage portion have been created by a stepof creating filters based on sample input signals and are correlatedwith power spectra of the sample input signals, wherein the secondfilters stored in said second filter storage portion have been createdby said step of creating filters and are correlated with S/Ns of thesample input signals, and wherein during said step of creating filters,a filter of an arbitrary distribution function G₀ is expanded into aseries of n filter elements, where n is an arbitrary number, each ofwhich is the difference between two distribution functions, coefficientsof the filter elements are set at will, the filter elements aremultiplied by the coefficients, respectively, and summed up to createthe first filters being a function of n, where n is the number of thefilter elements, and of the coefficients of the filter elements, thedistribution function G_(n) of the nth order obtained when expanding thefilter into the n filter elements and the distribution function G₀ arecombined together with arbitrary weight coefficients to create thesecond filters, and the value of n, the coefficients of the filterelements, and the weight coefficients are set based on the sample inputsignals.
 3. A method for signal processing as set forth in claim 2,wherein during said step of creating filters, the value of number n, thecoefficients of the filter elements, and the weight coefficients are setto maximize the S/Ns of the signals obtained by convolving the sampleinput signals using the created first and second filters.
 4. A methodfor signal processing as set forth in any one of claims 2 and 3, whereineach of said distribution functions is a Gaussian function.
 5. Anapparatus for signal processing, comprising: a first filter storageportion in which first filters created based on sample input signals andpower spectra of the sample input signals are correlatively stored; asecond filter storage portion in which second filters created based onsample input signals and S/Ns (signal-to-noise ratio) of the sampleinput signals are correlatively stored; a first filter selection portionfor calculating a power spectrum of an input signal, selecting a powerspectrum approximate to the calculated power spectrum from the powerspectra stored in the first filter storage portion, and selecting afirst filter corresponding to the selected power spectrum from the firstfilters stored in the first filter storage portion; a second filterselection portion for calculating a S/N of the input signal, selecting aS/N approximate to the calculated S/N from the S/Ns stored in the secondfilter storage portion, and selecting a second filter corresponding tothe selected S/N from the second filters stored in the second filterstorage portion; a third filter creation portion for creating a thirdfilter by summing up the selected first and second filters; and aconvolutional processing portion for convolving the input signal usingthe created third filter.
 6. An apparatus for signal processing as setforth in claim 5, wherein there is further provided a filter creationportion for creating the first and second filters based on the sampleinput signals and calculating power spectra and S/Ns of the sample inputsignals, and wherein said filter creation portion expands a filter of anarbitrary distribution function G₀ into a series of n filter elements,where n is an arbitrary number, each of which is the difference betweentwo distribution functions, sets coefficients of the filter elements atwill, multiplies the filter elements by the coefficients, respectively,and sums up the multiplied filter elements to create the first filterthat is a function of the number of the filter elements n and of thecoefficients of the filter elements, combines together a distributionfunction G_(n) of the nth order obtained when expanding the filter intothe n filter elements and the distribution function G₀ with an arbitraryweight coefficient to create the second filter, and sets the value of n,the coefficients of the filter elements, and the weight coefficientbased on the sample input signals.
 7. An apparatus for signal processingas set forth in claim 6, wherein said filter creation portion sets thevalue of the number n, the coefficients of the filter elements, and theweight coefficients to maximize the S/N of the signals obtained byconvolving the sample input signals using the created first and secondfilters.
 8. An apparatus for signal processing as set forth in any oneof claims 6 and 7, wherein each of said distribution functions is aGaussian function.